GENERALIZED PROPAGATION TECHNIQUES FOR LONGITUDINALLY VARYING REFRACTIVE-INDEX DISTRIBUTIONS

We demonstrate that our recently developed high-order expressions for the exponential of the sum of two noncommuting operators in terms of products of exponentials of the individual operators can be employed to generate rapid solution algorithms for a wide variety of parabolic differential equations. These include the Fresnel equation for longitudinally varying optical refractive index distributions and the mathematically equivalent Shrodinger equation for time-varying quantum-mechanical potential functions.